多项式的创建和相加

1. 多项式的创建

多项式链表是一个有序表，每项的位置要经过比较才能确定

2.多项式相加

设p1和p2分别指向Pa和Pb的当前结点，逐一比较两个结点的指数项，对于指数项相同的项，对应系数相加，若和不为0，则将他插入“和多项式”的链表中去；对于指数不相同的项，则通过比较将指数值较小的项插入到“和多项式”链表中去。Pa为“和多项式”，最后把Pb delete掉。

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代码如下：

/*用链表实现多项式的相加*/
#include<iostream>
using namespace std;

//单项式、多项式的定义
struct PNode
{
	float coef;//系数
	int expn;//指数
	PNode *next;
};
typedef PNode* Polynomial;

//多项式的创建
void CreatePolyn(Polynomial &P, int n)
{
	P = new PNode;
	P->next = NULL;
	PNode *pre = P;
	PNode *q = P->next;
	for (int i = 0; i < n; i++)
	{
		PNode *s = new PNode;
		cout << "请输入第" << i + 1 << "个单项式的系数：";
		cin >> s->coef;
		cout << "请输入第" << i + 1 << "个单项式的指数：";
		cin >> s->expn;
		pre = P;
		q = P->next;
		while (q&&q->expn<s->expn)
		{
			pre = q;
			q = q->next;
		}
		s->next = q;
		pre->next = s;
	}
}

void AddPolyn(Polynomial &Pa,Polynomial &Pb)
{
	PNode *p1 = Pa->next;
	PNode *p2 = Pb->next;
	PNode *p3 = Pa;
	while (p1&&p2)
	{
		if (p1->expn == p2->expn)
		{
			float sum = p1->coef + p2->coef;
			if (sum != 0)
			{
				p1->coef = sum;
				p3->next = p1;
				p3 = p1;
				p1 = p1->next;
				PNode *r = p2;
				p2 = p2->next;
				delete r;
			}
			else
			{
				PNode *r = p1; p1 = p1->next; delete r;
				r = p2; p2 = p2->next; delete r;
			}
		}
		else if (p1->expn < p2->expn)
		{
			p3->next = p1;
			p3 = p1;
			p1 = p1->next;
		}
		else
		{
			p3->next = p2;
			p3 = p2;
			p2 = p2->next;
		}
	}
	p3->next = p1 ? p1 : p2;
	delete Pb;
}


void Print(Polynomial P)
{
	if (P->next)
	{
		if (P->next->coef > 0)
			cout << P->next->coef << "x^" << P->next->expn;
		if (P->next->coef < 0)
			cout << P->next->coef << "x^" << P->next->expn;
	}
	PNode *p = P->next->next;
	while (p)
	{
		if (p->coef > 0)
			cout << "+" << p->coef<<"x^"<<p->expn;
		if (p->coef < 0)
			cout << p->coef << "x^" << p->expn;
		p = p->next;
	}
	cout << endl;
}


int main()
{
	Polynomial Pa,Pb;
	cout << "创建Pa：" << endl;
	CreatePolyn(Pa,2);
	cout << "Pa=";
	Print(Pa);

	cout << "创建Pb：" << endl;
	CreatePolyn(Pb, 2);
	cout << "Pb=";
	Print(Pb);

	AddPolyn(Pa, Pb);
	cout << "Pa+Pb=";
	Print(Pa);

	system("pause");
	return 0;
}